Supplemental materials for: Rolek, B.W., McClure, CJW, Dunn, L., Curti, M., … Ridgway’s Hawk IPM and PVA
Contact information: rolek.brian@peregrinefund.org
Metadata, data, and scripts used in analyses can be found at https://github.com/The-Peregrine-Fund/XXXXX.
The full workflow below is visible as a html website at: https://the-peregrine-fund.github.io/XXXXX/.
A permanent archive and DOI is available at: https://zenodo.org/doi/XXXXX
#load("C:\\Users\\rolek.brian\\OneDrive - The Peregrine Fund\\Documents\\Projects\\Ridgways IPM\\outputs\\ipm_sites.rdata")
load("C:\\Users\\rolek.brian\\OneDrive - The Peregrine Fund\\Documents\\Projects\\Ridgways IPM\\outputs\\ipm_statespace.rdata")
load("data/data.rdata")
library ('MCMCvis')
library ('coda')
library ('ggplot2')
library('reshape2')
out <- list(as.mcmc(post[[1]]),
as.mcmc(post[[2]]),
as.mcmc(post[[3]]),
as.mcmc(post[[4]]),
as.mcmc(post[[5]]),
as.mcmc(post[[6]]),
as.mcmc(post[[7]]),
as.mcmc(post[[8]]),
as.mcmc(post[[9]]),
as.mcmc(post[[10]]) )
# Identify chains with NAs that
# failed to initialize
NAlist <- c()
for (i in 1:length(out)){
NAlist[i] <- any (is.na(out[[i]][,1:286]) | out[[i]][,1:286]<0)
}
# Subset chains to those with good initial values
out <- out[!NAlist]
post2 <- post[!NAlist]
outp <- MCMCpstr(out, type="chains")
# default settings for plots
plt <- function(object, params,...) {
MCMCplot(object=out,
params=params,
guide_axis=TRUE,
HPD=TRUE, ci=c(80, 95), horiz=FALSE,
#ylim=c(-10,10),
...)
}
Plot model estimates of demographic rates. Life Stages are abbreviated as B = breeder, NB = nonbreeder, FY = first year. First-year abundance accounts for translocated birds.
# Abundance of females at Los Haitises
par(mfrow=c(4,2))
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("NFY[",1:13, ", 1]"),
main="First-year (FY)\n Los Haitises",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plot(2011:2023, datl$counts[1,,1]+constl$hacked.counts[,1],
ylab="Counts", type="b")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("NF[",1:13, ", 1]"),
main="Adult nonbreeder (NB)\n Los Haitises",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plot(2011:2023, datl$counts[2,,1],
ylab="Counts", type="b")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("NB[",1:13, ", 1]"),
main="Adult breeder (B)\n Los Haitises",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plot(2011:2023, datl$counts[3,,1],
ylab="Counts", type="b")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("Ntot[",1:13, ", 1]"),
main="All stages\n Los Haitises",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plot(2011:2023, colSums(datl$counts[,,1]),
ylab="Counts", type="b")
# Abundance of females at Punta Cana
par(mfrow=c(4,2))
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("NFY[",1:13, ", 2]"),
main="First-year (FY)\n Punta Cana",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plot(2011:2023, datl$counts[1,,2]+constl$hacked.counts[,2],
ylab="Counts", type="b")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("NF[",1:13, ", 2]"),
main="Adult nonbreeder (NB)\n Punta Cana",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plot(2011:2023, datl$counts[2,,2],
ylab="Counts", type="b")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("NB[",1:13, ", 2]"),
main="Adult breeder (B)\n Punta Cana",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plot(2011:2023, datl$counts[3,,2],
ylab="Counts", type="b")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("Ntot[",1:13, ", 2]"),
main="All stages\n Punta Cana",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plot(2011:2023, colSums(datl$counts[,,2]),
ylab="Counts", type="b")
Population dynamics are determined by transitions, These transitions between stages are abbreviated as the starting life stage to the final life stage. For example a first-year recruiting to a breeder would be abbreviated as “FY to B”. I’ll list them here for convenience:
“FY to NB” is first-year to nonbreeder.
“NB to NB” is nonbreeder adult to nonbreeder adult.
“B to NB” is a breeding adult to a nonbreeder adult.
“FY to B” is first-year to breeder.
“NB to B” is nonbreeder adult to breeder adult.
“B to B” is breeder adult to breeder adult.
# Finer population segments
par(mfrow=c(4,2))
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 1, ", ", 1:13, ", 1]"),
main="Los Haitises\nFirst-years born",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 2, ", ", 1:13, ", 1]"),
main="Los Haitises\nFY to NB",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 3, ", ", 1:13, ", 1]"),
main="Los Haitises\nNB to NB",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 4, ", ", 1:13, ", 1]"),
main="Los Haitises\nB to NB",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 5, ", ", 1:13, ", 1]"),
main="Los Haitises\nFY to B",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 6, ", ", 1:13, ", 1]"),
main="Los Haitises\nNB to B",
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 7, ", ", 1:13, ", 1]"),
main="Los Haitises\nB to B",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
par(mfrow=c(4,2))
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 1, ", ", 1:13, ", 2]"),
main="Punta Cana\nFY born",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 2, ", ", 1:13, ", 2]"),
main="Punta Cana\nFY to NB",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 3, ", ", 1:13, ", 2]"),
main="Punta Cana\nNB to NB",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 4, ", ", 1:13, ", 2]"),
main="Punta Cana\nB to NB",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 5, ", ", 1:13, ", 2]"),
main="Punta Cana\nFY to B",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 6, ", ", 1:13, ", 2]"),
main="Punta Cana\nNB to B",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
plt(object=out,
exact=TRUE, ISB=FALSE,
params=paste0("N[", 7, ", ", 1:13, ", 2]"),
main="Punta Cana\nB to B",
labels = 2011:2023,
xlab = "Year", ylab= "Abundance")
Other parameter estimates.
# I needed to abbreviate to save plot space
# FY=first-year, NB=Nonbreeder, B=Breeder
par(mfrow=c(1,2))
plt(object=out,
params=paste0("mus[",1:8, ", 1]"),
exact=TRUE, ISB=FALSE,
ylim=c(0,1),
main="Overall means\n Los Haitises",
labels=c("FY survival", "NB survival", "B survival",
"FY to B", "NB to B", "B to NB",
"NB detection", "B detection")
)
plt(object=out,
params=paste0("mus[",1:8, ", 2]"),
exact=TRUE, ISB=FALSE,
ylim=c(0,1),
main="Overall means\n Punta Cana",
labels=c("FY survival", "NB survival", "B survival",
"FY to B", "NB to B", "B to NB",
"NB detection", "B detection"))
par(mfrow=c(1,1))
plt(object=out,
params="betas",
main= "Translocation effects",
labels=c("FY survival", "NB survival", "B survival",
"FY to B", "NB to B", "B to NB",
"NB detection", "B detection"))
par(mfrow=c(1,1))
sds <- paste0("sds[", 1:9, "]")
plt(object=out, params=sds,
exact=TRUE, ISB=FALSE,
main="Temporal SDs (synchrony among sites)",
labels=c("FY survival", "NB survival", "B survival",
"FY to B", "NB to B", "B to NB",
"NB detection", "B detection",
"Fecundity"))
sds2 <- paste0("sds2[", 1:9, "]")
plt(object=out, params=sds2,
exact=TRUE, ISB=FALSE,
main="Site-temporal SDs",
labels=c("FY survival", "NB survival", "B survival",
"FY to B", "NB to B", "B to NB",
"NB detection", "B detection",
"Fecundity"))
# Correlations among vital rates
# Plot is messy with only a few strong correlations
ind <- 1
Rs <- R2s <- c()
for (i in 1:(nrow(outp$R)-1)){
for (j in (i+1):nrow(outp$R)){
Rs[ind] <- paste0("R[",i,", ", j, "]")
R2s[ind] <- paste0("R2[",i,", ", j, "]")
ind <- ind+1
}}
par(mfrow=c(1,1))
plt(object=out, params=Rs, exact=TRUE, ISB=FALSE,
main="Correlations btw demographic rates\n over time (synchrony)",
xlab = "Rhos", guide_lines=TRUE)
plt(object=out, params=R2s, exact=TRUE, ISB=FALSE,
main="Correlations btw demographic rates\n over time and sites",
xlab = "Rhos", guide_lines=TRUE)
# lmu.brood = mean brood size (log scale),
# sig.brood = SD among nests
# mu.nest = mean nest success
par(mfrow=c(1,1))
plt(object=out,
params=c("lmu.f"),
labels= c("Fecundity\n(log scale)\nLos Haitises",
"Fecundity\n(log scale)\nPunta Cana"))
# gamma = nest treatment effect on fecundity
plt(object=out,
params=c("gamma"),
main="Anti-Parasitic Fly\nTreatment Effects", ylim=c(0,3))
# Annual averages for integration into the population model
labs <- c(paste0("LH ",2011:2023), paste0("PC ",2011:2023))
plt(object=out, params="mn.phiFY", ylim=c(0,1),
main="First-year survival", labels = labs,
xlab = "Year", ylab= "Survival")
abline(v=13.5, lwd=2)
plt(object=out, params="mn.phiA", ylim=c(0,1),
main="Adult nonbreeder", labels = labs,
xlab = "Year", ylab= "Survival")
abline(v=13.5, lwd=2)
plt(object=out, params="mn.phiB", ylim=c(0,1),
main="Breeder", labels = labs,
xlab = "Year", ylab= "Survival")
abline(v=13.5, lwd=2)
plt(object=out, params="mn.psiFYB", ylim=c(0,1),
main="First-year to breeder", labels = labs,
xlab = "Year", ylab= "Recruitment")
abline(v=13.5, lwd=2)
plt(object=out, params="mn.psiAB", ylim=c(0,1),
main="Adult nonbreeder to breeder", labels = labs,
xlab = "Year", ylab= "Recruitment")
abline(v=13.5, lwd=2)
plt(object=out, params="mn.psiBA", ylim=c(0,1),
main="Adult breeder to nonbreeder", labels = labs,
xlab = "Year", ylab= "Recruitment")
abline(v=13.5, lwd=2)
plt(object=out, params="mn.pA", ylim=c(0,1),
main="Nonbreeder", labels = labs,
xlab = "Year", ylab= "Detection")
abline(v=13.5, lwd=2)
plt(object=out, params="mn.pB", ylim=c(0,1),
main="Breeder", labels = labs,
xlab = "Year", ylab= "Detection")
abline(v=13.5, lwd=2)
plt(object=out, params="mn.f",
main="", labels=labs,
xlab = "Year", ylab= "Fecundity")
abline(v=13.5, lwd=2)
mdFY <- apply(outp$NFY, c(1,2), median)
mdB <- apply(outp$NB, c(1,2), median)
mdF <- apply(outp$NF, c(1,2), median)
lFY <- melt(mdFY)
lB <- melt(mdB)
lF <- melt(mdF)
lFY$Stage <- "First-year"
lB$Stage <- "Breeder"
lF$Stage <- "Nonbreeder"
ldat <- rbind(lFY, lB, lF)
colnames(ldat)[1:3] <- c("Year", "Sitenum", "Number")
ldat$Site <- ifelse(ldat$Sitenum==1, "Los Haitises", "Punta Cana")
# Use median number of females in each stage
# to plot an approximate population structure
ggplot(ldat, aes(fill=Stage, y=as.numeric(Number), x=Year)) +
geom_bar(position="fill", stat="identity") +
ylab("Proportion of population") +
facet_wrap("Site")
ggplot(ldat, aes(fill=Stage, y=as.numeric(Number), x=Year)) +
geom_bar(position="stack", stat="identity") +
ylab("Numer of females") +
facet_wrap("Site", scales = "free_y")
Parameter estimates for input into a population viability analysis.
pars1 <- c("sds", "sds2","mus", "betas",
"NFY", "NF", "NB", "Ntot",
"mn.phiFY","mn.phiA", "mn.phiB",
"mn.psiFYB", "mn.psiAB", "mn.psiBA",
"mn.pA", "mn.pB")
# Estimates for the survival model
# In this order: FY survival, NB survival, B survival,
# FY to B recruitment, NB to B recruitent, B to NB recruitment,
# Detection NB, Detection B
MCMCsummary(post2, params = c(sds, sds2),
exact=TRUE, ISB=FALSE,
digits=2, HPD = T,
hpd_prob = 0.80, pg0= TRUE)
# Mus are means for
# mus[1, site] , where site=1 is LH and site=2 is PC
# Survival of first years = mus[1,]
# Survival of nonbreeders = mus[2,]
# Survival of breeders = mus[3,]
# Breeding propensity of first years = mus[4,]
# Breeding propensity of nonbreeders = mus[5,]
# Transition from breeder to nonbreeder = mus[6,]
# Detection probability of nonbreeders = mus[7,]
# Detection probability of breeders
MCMCsummary(post2, params = pars1[3:4],
digits=3, HPD = T,
hpd_prob = 0.80, pg0= TRUE)
# Estimates of population size
# NFY= first year,
# NF = nonbreeders,
# NB=breeders,
# Ntot=total
# All are presented as N[time, site],
# where time 1=2011 ... 13=2023,
# site 1 = LH and site 2=PC
MCMCsummary(post2, params = pars1[5:8],
digits=2, HPD = T,
hpd_prob = 0.80, pg0= TRUE)
MCMCsummary(post2, params = pars1[9:16],
digits=2, HPD = T,
hpd_prob = 0.80, pg0= TRUE)
# Correlations among demographic rates time (synchrony)
MCMCsummary(post2, params = "R",
digits=2, HPD = T,
hpd_prob = 0.80, pg0= TRUE)
# Correlations among demographic rates site x time
MCMCsummary(post2, params = "R2",
digits=2, HPD = T,
hpd_prob = 0.80, pg0= TRUE)
Goodness-of-fit tests provide evidence that statistical distributions adequately describe the data. Here we test fit for brood size and counts. A Bayesian p-value nearest to 0.5 suggests good fitting statistical distributions, while values near 1 or 0 suggest poor fit.
# Goodness of fit check
fit.check <- function(out, ratio=FALSE,
name.rep="f.dmape.rep",
name.obs="f.dmape.obs",
jit=100,
ind=1,
lab=""){
par(mfrow=c(1,1))
# plot mean absolute percentage error
samps <- MCMCpstr(out, "all", type="chains")
rep <- samps[name.rep][[1]][ind,]
obs <- samps[name.obs][[1]][ind,]
mx <- max(c(rep, obs))
mn <- min(c(rep, obs))
plot(jitter(obs, amount=jit),
jitter(rep, amount=jit),
main=paste0("Mean absolute percentage error\n",lab),
ylab="Discrepancy replicate values",
xlab="Discrepancy observed values",
xlim=c(mn,mx), ylim=c(mn,mx),
pch=16, cex=0.5, col="gray10")
curve(1*x, from=mn, to=mx, add=T, lty=2, lwd=2, col="blue")
bp1 <- round(mean(rep > obs),2)
loc <- ifelse(bp1 < 0.5, "topleft", "bottomright")
legend(loc, legend=bquote(p[B]==.(bp1)), bty="n", cex=2)
if (ratio==TRUE){
t.rep <- samps["tvm.rep"][[1]][ind,]
t.obs <- samps["tvm.obs"][[1]][ind,]
# plot variance/mean ratio
hist(t.rep, nclass=50,
xlab="variance/mean ", main=NA, axes=FALSE)
abline(v=t.obs, col="red")
axis(1); axis(2)
}
return(list('Bayesian p-value'=bp1))
}
# check goodness-of-fit for brood size
# breeder, ind=1
fit.check(out, ratio=F,
name.rep="dmape.rep",
name.obs="dmape.obs",
ind=1,
lab="Breeder counts- Poisson", jit=300)
## $`Bayesian p-value`
## [1] 0.35
# nonbreeder, ind=2
fit.check(out, ratio=F,
name.rep="dmape.rep",
name.obs="dmape.obs",
ind=2,
lab="Breeder counts- Poisson", jit=300)
## $`Bayesian p-value`
## [1] 0.45
# first-year, ind=3
# poisson failed fit test bp=0
# Currently running models to try and fix
fit.check(out, ratio=F,
name.rep="dmape.rep",
name.obs="dmape.obs",
ind=3,
lab="First-year counts\nNeg binomial-Poisson", jit=300)
## $`Bayesian p-value`
## [1] 0.47
# fecundity
fit.check(out, ratio=F,
name.rep="f.dmape.rep",
name.obs="f.dmape.obs",
ind=1,
lab="Fecundity-Neg binomial", jit=300)
## $`Bayesian p-value`
## [1] 0.37
Traceplots provide evidence that models adequately converged.
MCMCtrace(post2, pdf=FALSE, params= sds, exact=TRUE, ISB=FALSE)
MCMCtrace(post2, pdf=FALSE, params= sds2, exact=TRUE, ISB=FALSE)
MCMCtrace(post2, pdf=FALSE, params= "mus")
MCMCtrace(post2, pdf=FALSE, params= "betas")
MCMCtrace(post2, pdf=FALSE, params= "NF")
MCMCtrace(post2, pdf=FALSE, params= "NFY")
MCMCtrace(post2, pdf=FALSE, params= "NB")
MCMCtrace(post2, pdf=FALSE, params= "R")